Question: Simplify the following expression: $p = \dfrac{q^2 - 15q + 50}{q - 5} $
Answer: First factor the polynomial in the numerator. $ q^2 - 15q + 50 = (q - 5)(q - 10) $ So we can rewrite the expression as: $p = \dfrac{(q - 5)(q - 10)}{q - 5} $ We can divide the numerator and denominator by $(q - 5)$ on condition that $q \neq 5$ Therefore $p = q - 10; q \neq 5$